Currents in different parts of resistor

Please refer my attachments, revered members.
In Step 2 the 4 ohm resistor is removed, its been mentioned that no current will go through any resistor. Why? Still current can flow through the 4 ohm resistor that is connected in the right extreme end, can't it?
Again, it has been mentioned that if 4 ohm resistor is added between d and e, no current will be drawn into it. Can i know why?

Current through a resistor equals the voltage across the resistor divided by the resistor's resistance. Since both e and d are at the same voltage, no current would flow through a resistor connected across those points in the circuit..

Current through a resistor equals the voltage across the resistor divided by the resistor's resistance. Since both e and d are at the same voltage, no current would flow through a resistor connected across those points in the circuit..

Thanks for the reply sir.
I = V/R. The extreme left resistor of resistance 4 ohm is connected to voltage of 2V. So current is 2/4 that gives 0.5 A of current. How then we conclude no current is flowing through any of the resistor?

Thanks sir.
But the point d is connected to the positive terminal of the battery and point b is to negative terminal. If we assume the potential at b to be zero then Vd is 2-0 so 2V. How it is zero as mentioned by you, sir?

Sorry for confusion. I did not notice that you already have Vd on the diagram.
So let as start again
The voltage difference between point a and b is equal to :
Vac = Va - Vc = 2V - 2V = 0V
And this means that no current can flow between point a and c. So, no current in left and right resistor.
I = Vac/(4Ω + 4Ω) = 0V/8Ω = 0A
If this is the case the voltage at point e is also equal to 2V
Ve = Va - I*4Ω = 2V - 0A*2Ω = 2V
And the middle resistor current is Im = (Ve - Vd)/Rm = (2V - 2V)/4Ω = 0A

Thanks for the reply sir.
I = V/R. The extreme left resistor of resistance 4 ohm is connected to voltage of 2V. So current is 2/4 that gives 0.5 A of current. How then we conclude no current is flowing through any of the resistor?

You are making one of the classic mistakes and throwing the nearest V and the neared R at Ohm's Law and getting an irrelevant value that happens to have the units of current because you aren't paying attention to what Ohm's Law means. You need the voltage ACROSS the resistor -- not the value of some battery that happens to be connected to one side of it.

You are making one of the classic mistakes and throwing the nearest V and the neared R at Ohm's Law and getting an irrelevant value that happens to have the units of current because you aren't paying attention to what Ohm's Law means. You need the voltage ACROSS the resistor -- not the value of some battery that happens to be connected to one side of it.